{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "rcParams['savefig.dpi']=100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import  stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "chisq=stats.chi2(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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hnTMwbwMuz73qdoyk9YHLO3nMDvKdSGZmZsMw5AATEQ8A3wGuzQMwVk7S3qQx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\nvKV21LluAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x67e0b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=subplots()\n",
    "xi = np.linspace(0.01,10,100)\n",
    "ax.plot(xi,chisq.pdf(xi),color='k',lw=2)\n",
    "ax.axis(ymax=1)\n",
    "ax.set_xlabel('$x$',fontsize=18)\n",
    "ax.set_ylabel('$f_x(x)$',fontsize=22)\n",
    "ax.set_title(r'$\\chi_1^2$ Probability Density',fontsize=18,fontdict={'family':'serif'})\n",
    "fig.savefig('../fig-probability/ProbabilityInequalities_001.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cjKsgdln0/t6ysKfhplSV1mdsxhhjTBPTElcr5HVNrYBcFakkBltwhUGi58d2o+oCKNWZ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\n1OX/AANVrA763K4aAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x68a9e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=subplots()\n",
    "ax.plot(xi,1-chisq.cdf(xi),label=r'$\\mathbb{P}(X>\\epsilon)$',color='k',linestyle='-',lw=3)\n",
    "ax.plot(xi,1/xi,label=r'$\\mathbb{E}(X)/\\epsilon$',lw=3,color='k',ls='--')\n",
    "ax.fill_between(xi,1-chisq.cdf(xi),1/xi,color='gray',alpha=.3)\n",
    "ax.axis(ymax=.5)\n",
    "ax.set_xlabel('$\\epsilon$',fontsize=18)\n",
    "ax.legend(fontsize=18)\n",
    "ax.set_title(\"Markov's Inequality\",fontsize=18)\n",
    "fig.savefig('../fig-probability/ProbabilityInequalities_002.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chisq.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy.integrate import quad\n",
    "rv = stats.chi2(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# from sympy import init_printing;init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sympy\n",
    "from sympy import stats as ss\n",
    "t = sympy.symbols('t',real=True,positive=True)\n",
    "# z = sympy.symbols('z',real=True,positive=True)\n",
    "\n",
    "x=ss.ChiSquared('x',1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# v=ss.P((x-1) > t,x>1)+ss.P(-(x-1) > t,x<1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "w=(1-ss.cdf(x)(t+1))+ ss.cdf(x)(1-t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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i8msR+Y2IvC8iP6j5qOTPxdQskj8abYBGhHWoA/ZSxZKo7pK/k4FXgCKcRVIO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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xdd94190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=subplots()\n",
    "fw=sympy.lambdify(t,w)\n",
    "ti = np.linspace(.01,5)\n",
    "fvals = map(fw,ti)\n",
    "ax.plot(ti,fvals,'k',lw=3,label=r'$\\mathbb{P}(\\vert X-\\mu\\vert > \\epsilon)$')\n",
    "ax.plot(ti,4/ti**2,'k--',lw=3,label=r'$\\sigma^2/\\epsilon^2$')\n",
    "ax.fill_between(ti,fvals,4/ti**2,color='gray',alpha=.3)\n",
    "ax.axis(ymax=1)\n",
    "ax.set_xlabel('$\\epsilon$',fontsize=18)\n",
    "ax.set_title(\"Chebyshev's Inequality\")\n",
    "ax.legend(fontsize=16)\n",
    "fig.savefig('../fig-probability/ProbabilityInequalities_003.png',dpi=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%qtconsole"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# from sympy.interactive import printing\n",
    "# printing.init_printing(use_latex=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\begin{cases} \\operatorname{erf}{\\left (\\frac{\\sqrt{2}}{2} \\sqrt{- t + 1} \\right )} & \\text{for}\\: - t + 1 \\geq 0 \\\\0 & \\text{otherwise} \\end{cases} - \\begin{cases} \\operatorname{erf}{\\left (\\frac{\\sqrt{2}}{2} \\sqrt{t + 1} \\right )} & \\text{for}\\: t + 1 \\geq 0 \\\\0 & \\text{otherwise} \\end{cases} + 1$$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Math\n",
    "Math(sympy.latex(w))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\begin{cases} \\operatorname{erf}{\\left (\\frac{\\sqrt{2} \\sqrt{t}}{2} \\right )} & \\text{for}\\: t \\geq 0 \\\\0 & \\text{otherwise} \\end{cases}$$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Math(sympy.latex(ss.cdf(x)(t)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Hoeffding’s Inequality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xe563210>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LAbNq2Re4MoKFuYO0kwieBm7A3QNmpbkQMKsIiY2BN+FugYG6DHinxCq5g5i1ExcCZtWx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\nZmZWY/8fHWrXTl7lCssAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe50c930>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from  scipy.integrate import quad\n",
    "from scipy.interpolate import  interp1d\n",
    "\n",
    "def pdf(n=3,m=20):\n",
    "    u = np.ones(m)\n",
    "    fv=reduce(lambda i,j:np.convolve(i,j),[u,]*n,u)\n",
    "    xv = np.linspace(0,n,len(fv))\n",
    "    norm = (xv[1]-xv[0])*sum(fv)\n",
    "    xv = xv-np.mean(xv)\n",
    "    return interp1d(xv,fv/norm,fill_value=0,bounds_error=False)\n",
    "\n",
    "f3=pdf(5)\n",
    "apdf=interp1d(f3.x[f3.x>=0],f3.y[f3.x>=0]*2,fill_value=0,bounds_error=False)\n",
    "\n",
    "ti = linspace(0.01,f3.x.max(),50)\n",
    "\n",
    "plot(f3.x,f3.y,'-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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zs2E/cJ6qvqKqM1V1Ds6bdknXSvga5xHLGTiDHCuFHFuL8/7SKvQEEWmAM3jy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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe9b4e70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=subplots()\n",
    "\n",
    "vals = map(lambda t:quad(apdf,t,100)[0],ti)\n",
    "ax.plot(ti,vals,'-k',label=r'$\\mathbb{P}(\\vert \\overline{X}_n-1/2\\vert \\geq \\epsilon)$',lw=3)\n",
    "ax.plot(ti,2*np.exp(-2*ti**2),label='Hoeffding',color='k',ls='--',lw=3)\n",
    "ax.fill_between(ti,vals,2*np.exp(-2*ti**2),color='gray',alpha=0.3)\n",
    "ax.plot(ti,0.52/ti,label='Markov',color='k',ls=':')\n",
    "ax.legend(loc=0,fontsize=12)\n",
    "ax.axis(ymax=2)\n",
    "ax.set_xlabel('$\\epsilon$',fontsize=18)\n",
    "fig.savefig('../fig-probability/ProbabilityInequalities_004.png',dpi=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
